James Nelson, lecturer in Statistical Science, University College London

James Nelson joined the Department of Statistical Science at University College London as a lecturer in 2010. After a PhD in applied harmonic analysis from the Mathematics Department at Anglia Polytechnic University (1998-2001), he held post-doc positions in: the Applied Mathematics and Computing Group at the University of Cranfield (2001-2004); the Information: Signals, Images, and Systems Research Group at the University of Southampton (2004-2006); and the Signal Processing and Communications Laboratory at the University of Cambridge (2006-2010).


Research Interests:

Wavelet analysis, statistical signal and image processing, random fields, and machine learning. In particular: wavelet/Riesz basis construction and sparsity with applications to detection and classification; Markov random fields; multiresolution analysis for machine learning, support vector machine kernel construction for pattern recognition; sampling theory; and (multi-)fractal dimension and Hurst index estimation for texture and volatility models.


Selected Research Activity

Hyperparameter search reduction for Paley-Weiner reproducing Mercer kernels (01/2005-12/2006)

During the "Data and Information Fusion, Defence Technology Centre" (DIF-DTC) Phase I project, we developed adaptive hyper- and multi-spectral data fusion methods for target detection and tracking and biometric identification in collaboration with the UK Ministry of Defence, QinetiQ, and General Dynamics UK.

The work included the development of a framework to reduce the choice of optimal support vector machine kernel hyperparameters to a finite/small set. Previous methods relied upon sub-optimal ad-hoc grid searches and cross validation. We achieved an a priori parameter subset estimation by bringing together two differing philosophies of data analysis, namely machine learning and applied harmonic analysis, and asserting the weak condition that the decision function belongs to a Paley-Weiner space; and using "sequency analysis" to estimate its support. This lead to enhanced methods and state-of-the-art results for hyperspectral classification. The work was subsequently extended to the sequence kernel case (to deal with data of differing lengths) and applied to a speaker recognition problem.

 
Rotation invariant dual-tree wavelet detector and particle filtering (12/2006-10/2009)

The Data and Information Fusion, Defence Technology Centre Phase II project was carried out in collaboration with the UK Ministry of Defence, QinetiQ, General Dynamics UK, Waterfall Solutions, the University of Cambridge, Imperial College London, and University of Bristol.

Our task in this project was to develop the application of dual-tree complex wavelet polar matching and particle filtering to shift and rotation invariant object detection. These methods were used to detect and track objects of interest from aerial imagery in both electro-optical and infra red spectrums. A notable feature was that the algorithm adapted to the visibility of the target. In experiments, this allowed the tracker to reacquire the target after prolonged periods of total occlusion. The shift and scale tolerance of the polar matching detector was then enhanced by exploiting the sesquilinear form of the polar matching operator and the geometry of the feature vectors and corresponding Jacobians. Aside from offering an observational model to trackers, such detectors can be used to facilitate both keypoint matching and neighbourhood search detection.

 

Wavelet shrinkage for sonar imagery (10/2009-present)

During 10/2009-10/2010, I was the researcher co-investigator for a University Defence Research Centre project co-funded by the EPSRC and Dstl. This work was continued into my appointment at UCL via consultancy and a short contract.

 In this project, dual-tree wavelets were applied to the estimation of anisotropic fractal dimension. A wavelet shrinkage method was then developed that improved the detection of mines in sonar imagery by reducing the false positives caused by sand ripples. By modelling the background as stochastic self-similar random field, principled features were devised to construct a scale invariant likelihood model of ripples. This was later extended by incorporating a Markov random field model to exploit the observation that rippled and non-rippled locations are unlikely to appear at isolated points. In this framework, the likelihood function is designed to "soft-shrink" coefficients according to the energy ratio value; the prior (Ising model) encodes spatial constraints into the shrinkage functions. Markov Chain Monte Carlo methods provided an efficient, tractable way to estimate the conditional distribution of the posterior marginal ripple/non-ripple state in the dual-tree wavelet domain. Ripple suppression was then realised by multiplying the dual-tree wavelet coefficients by the marginal probabilities of the non-ripple states.

 

Fused Lasso and rotation invariant autoregressive models for texture classification (2012-present)

Inspired by discussions with Microsoft India and the University of Waterloo, the problem of rotation invariant texture classification was tackled by considering radially sampled autoregressive random field models. Unfortunately, owing to the strong correlations present in the neighbourhood covariate matrix, parameter estimation is complicated by the dichotomy between ill-conditionedness and rotation invariance. Exploiting the Fused Lasso framework, we proposed a compromise which incorporates two regularisers. The 1-norm induces stability and performs variable selection amongst strongly correlated radial samples; the total variation seminorm encourages clustering and promotes model parsimony. Experiments on standard datasets confirmed the potential utility and parallels were drawn within the texture classification literature and beyond. 

 

Sparse regularisation for piecewise, minimal codomain cardinality, Riesz basis construction (2012-present)

Piecewise, low-order polynomial, Riesz basis families were constructed such that they share the same coefficient functionals of smoother, orthonormal bases in a localised indexing subset. It was shown that a minimal cardinality basis codomain can be realised by inducing sparsity, via 1-norm regularisation, in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optmisation over a suitably large dictionary. Furthermore, it was shown that a subset of these solutions are equivalent to a specific, constrained analytical solution based on Sylvester-type Hadamard matrices. It is anticipated that these constructions are well suited for approximate signal processing and sparse representations. This work is currently under review in the journal: Applied Computational Harmonic Analysis (impact factor 3.5).

 

Multiresolution Markov random fields for mammogram imagery analysis (07/2012-present)

From July 2012, we have been developing a much needed multiresolution Bayesian approach to the problem of detecting radial patterns of spicules, an early sign of breast cancer in mammograms. This project involves collaboration with the Division of Medicine at UCL and UCL Hospital. We are investigating the construction of multiscale, directional regularity and phase congruence features, constrained by Markov-type priors. The proposed Bayesian wavelet shrinkage approach will be a significant departure from previous attempts and is designed to overcome the main shortcomings of heuristic thresholding (erroneous discontinuities and limited solution search space) found in present state-of-the-art spicule detection and orientation estimation methods.

 

Contact details and other info:

Please see James Nelson's UCL webpage

Publications

Please see James Nelson's personal UCL pages and Google Scholar